How to stack UV island using Python in Blender?
Here we need three things:

Find the 2d cursor position
Check the mode we are in before processing the UV coordinates
Use the UV layer to find UV coordinates

For each face, once UV coordinates are found, calculate their center and offset the coordinates by the difference from the cursor.
Note that if no UV editor opened, won't find the cursor and does nothing.
Commented code:
import bpy
from mathutils import Vector


def find_cursor_location():
    # Look through area and find the first image editor
    for area in bpy.context.screen.areas:
        if area.type == 'IMAGE_EDITOR':
            return area.spaces.active.cursor_location
    return None

obj = bpy.context.object
cursor = find_cursor_location()

if cursor:
    #Check the mode as we cant do it in edit mode
    mode = obj.mode
    if mode != 'OBJECT':
        bpy.ops.object.mode_set(mode='OBJECT')
        
    me = obj.data #Need to get it here in case mode is changed
    uv_layer = me.uv_layers.active

    if uv_layer:
        for poly in me.polygons:
            # Get all Uv coordinates of the face
            uvs = [uv_layer.data[loop_index].uv for loop_index in poly.loop_indices]
            # Its center
            center = sum(uvs, Vector((0,0))) / len(uvs)
            # The needed offset
            delta = center - cursor
            # Shift UV coords
            for uv_data in [uv_layer.data[loop_index] for loop_index in poly.loop_indices]:
                uv_data.uv -= delta

    #Back to the mode we were in
    if mode != 'OBJECT':
        bpy.ops.object.mode_set(mode=mode)